FORM OF THE BifiD. 



223 



sent a surface relatively less in birds of large size and of 

 great weight. 



The surprise which we feel at the result obtained by Mens, 

 de Lucy disappears when we consider that there is a geome- 

 trical reason why the surface of the wing cannot increase in 

 the ratio of the weight of the bird. In fact, if we take two 

 objects of the same form — two cubes, for example — one of 

 which has a diameter twice as large as the other, each of the 

 surfaces of the larger cube will be four times as large as that 

 of the smaller one, but the weight of the large cube will be 

 eight times that of the small one. 



Thus, for all similar geometrical solids, the linear dimen- 

 sions being in a certain ratio, the surfaces will increase in 

 proportion to their squares, and the weights in that of their 

 cubes. Two birds similar in form, one of which has an 

 extent of wing twice as large as the other, will have wiog 

 surfaces in the proportion of one to four, and weights in that 

 of one to eight. 



Dr. Hureau de Villeneuve, basing his enquiries on these 

 considerations, has determined the surface of wing which 

 would enable a bat having the weight of a man to fly ; and 

 he has found that each of the wings need not be three metres 

 in length. 



In a remarkable work on the relative extent of win^ and 

 weight of pectoral muscles in different species of flying ver- 

 tebrate animals,^' Hartings shows that in a series of birds we 

 can establish a certain relation between the surface of the 

 wing and the weight of the body. But we must be careful 

 only to compare elements which admit of comparison; for 

 instance, the length of the wings, the square roots of their 

 surfaces, and the cube roots of the weights of different birds. 



Let I be the length of the wing ; a, its area or surface ; 

 and p the weight of the body ; we can compare together \/a, 

 and yjp. 



Making observations on different types of birds, Hartings 

 ascertained their measurements and weights, from which he 

 obtained the following table : — 



* Archives Neeiiandaises, Yol. XIY., p. 1869. 



